How would the Uighurs run a country where they were the majority? Sadly, we have two governments, one(the Uighurs) believes in a warlike state where religion is the authority and another warlike one (China) where the secular state is the authority and China is larger.
These states that blend state and religious power all seem headed towards religious oligopolies - Iran comes to mind.
What happens when the states of Europe become majority Islamic? Will Islam undergo a gradual reformation or will the islamic governments insist on forced conversion?, as they have done in the past.
I do not know why they insist on control over others. Whatever end game follows, will be 100 years to fruition...
Attaching agreed-upon bad things like authoritarianism and terrorism and oppression onto arbitrary symbols like Islam and secularism is fallacious. Those superficial symbols make for terrible indicators of actual evil, and rhetoric like the above only serves to increase the injustice done to innocent people. See the recent Christchurch attack.
OP is right in observing that Islam is not compatible with political system in China. Islam has certain political goals built in. Chinese system requires political monopoly and keeping religion private matter. Hence the confrontation is logical and unavoidable.
Most Christian denominations I've encountered claim the same, and often even narrow that claim to their specific denomination (many Evangelicals believing that Catholics won't make the cut when it comes to going to heaven, for example).
